Nonadiabatic phonons within the doped graphene layers of $X{\text{C}}_6$ compounds

We report Raman-scattering measurements of ${\text{BaC}}_6$, ${\text{SrC}}_6$, ${\text{YbC}}_6$, and ${\text{CaC}}_6$, which permit a systematic study of the phonons and the electron-phonon interaction within the doped graphene layers of these compounds. The out-of-plane carbon phonon softens as the spacing of the graphene layers is reduced in the series ${\text{BaC}}_6$, ${\text{SrC}}_6$, ${\text{YbC}}_6$, and ${\text{CaC}}_6$. This is due to increasing charge in the ${\pi }^{\ast }$ electronic band. Electron-phonon interaction effects between the in-plane carbon modes at $\approx 1500{\text{cm}}^{-1}$ and the ${\pi }^{\ast }$ electrons cause a strong nonadiabatic renormalization. As charge is transferred into the ${\pi }^{\ast }$ band, these nonadiabatic effects are found to increase concurrent with a reduction in the phonon lifetime.

Figure 1

(Color online) The Raman spectra from different positions numbered on the GIC surface shown in the increased-contrast inset. Spot 1 corresponds to pure, ordered GIC with one ${\text{C}}_{xy}$ mode visible at $\approx 1500{\text{cm}}^{-1}$. Spots 2–4 also show the $\approx 1350{\text{cm}}^{-1}$ and the $\approx 1600{\text{cm}}^{-1}$ phonons which arise from sample disorder. All spectra are normalized to represent the same counting time.

Figure 2

(Color online) The Raman spectra of the ${\text{C}}_z$ modes for ${\text{BaC}}_6$, ${\text{SrC}}_6$, ${\text{YbC}}_6$, and ${\text{CaC}}_6$. Black dots represent the data points and the solid lines are the Lorentzian fits. A smooth background has been removed from the data. The inset shows the variation in peak position for the experimental frequency ${\omega }_0$ (dots) and the DFT value ${\omega }^A$ (crosses) (Ref. 13).

Figure 3

(Color online) The Raman spectra of the ${\text{C}}_{xy}$ modes for ${\text{CaC}}_6$, ${\text{YbC}}_6$, ${\text{SrC}}_6$, and ${\text{BaC}}_6$. Black dots are the measured spectrum, the thin line is the BWF function, the dotted lines are the surface contaminant and the fit is shown as a solid line. A linear background has been removed from the data and the spectra have been offset from one another for clarity.